One thing you should know first is that the order and letters of drives aren't set in stone. "C" doesn't HAVE to be your 2 TB hard drive. And as far as I know, Windows decides that whatever it's installed on is "C". Why would you care about the letters so much? Anyway, I think you can change all that in Disk Management once Windows is installed.
By default, and with how everyone has always been used to it, C is where Windows is, and other letters aren't. Honestly, I don't know why you would absolutely want your hard drive to be C.
Now, as for your question, no, you cannot move any Windows core files once the installation is complete. Well, you probably can, but you'll probably break Windows too if you do.
But what you CAN do, however, to reduce the amount of data and strain on the SSD, is to install Windows onto your SSD, and then move specific content to your HDD with symbolic links (for which I recommend Link Shell Extension) and/or registry changes.
The simplest way, which doesn't require making possibly risky registry changes, is to:
Redirect your Documents, Images, Videos, etc. libraries to user folders that you will create on your HDD. This will allow you to place your heavy files over to your larger hard drive and still be able to easily access them easily.
This method will indeed move your data, but it does not allow you to move your AppData folder, and thus save your SSD many writes (which reduce its lifespan a little). With modern SSDs, it's probably not a big deal, but if you want to move AppData, you will need to move your whole user profile folder over to your hard drive. To do that, you need a series of registry changes, which I am not confident enough to explain, so I must leave you to look it up. Certainly Super User has at least a couple of useful questions on the topic.
Transparently move selected larger programs (such as games) onto your HDD as explained below. Let's say that you are installing the game, ehm, Fatsy Birds by Rolyo Studios.
Before the program installs, on the screen where it asks you to select a destination folder, alt-tab to Windows Explorer and go
D:\Programs, a folder that you'll have created for your programs that you don't want to keep on your SSD.
There, create a new folder. To make sure everything is all right, you might want to use the default name that the installer suggests, but as long as you give the installer the same name as the folder you create, it should be fine.
In the case of the game I just invented, the installer will suggest
C:\Program Files (x86)\Rolyo Studios\Fatsy Birds. Then you should create the folder
Right click your newly created folder,
Rolyo Studios, and select the option "Pick Link Source".
Still in the Explorer, browse to
C:\Program Files (x86). Click an empty spot and select "Drop As..." and then "Symbolic Link". A new
Rolyo Studios "folder" should have appeared in your Program Files (x86) folder. This, however, is not a real folder. It's a link to your folder in "D". But programs don't know that. The redirection is complete. (Except for some rare programs, such as SkyDrive in Windows 8.1.)
Go back to the install wizard and install your new game in
C:\Program Files (x86)\Rolyo Studios\Fatsy Birds. Magic. For both you and the system, the game is on C, but its data is actually fetched over on D.
Note: In the instructions above, "C" is your SSD and "D" is your larger hard drive. The instructions are also assuming that you are using Link Shell Extension. If not, I assume you're using the CLI command
mklink and thus know what you're doing and don't need instructions.